Characteristic

Characteristic of a logarithm is the integer part of common logarithm (log base 10). Characteristic determines order of magnitude. For number N: If 1 ≤ N < 10, characteristic = 0 (log(5) ≈ 0.699); If 10 ≤ N < 100, characteristic = 1 (log(50) ≈ 1.699); If 0.1 ≤ N < 1, characteristic = -1 (log(0.5) ≈ -0.301). Rule: Characteristic of N = (number of digits before decimal - 1). For decimals: If 0.01 ≤ N < 0.1, characteristic = -2. Mantissa: decimal part, always positive (0 to 1). Shortcut: Count significant digits to find characteristic immediately. Exam tip: Characteristic helps locate decimal point in antilog answers. Remember: log(N) = characteristic + mantissa.